Which of the following is functionally complete?
which of the following is functionally complete?
- A.
⊕, not
- B.
⊕, 1, +
- C.
⊕, 1, not
- D.
⊙, 1, not
Attempted by 104 students.
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Correct answer: B
Functional completeness requires a set of operators capable of expressing all Boolean functions, typically including {AND, OR, NOT}.
Option 1 uses the set {⊕, 1, +}. The NOT operation can be derived as A ⊕ 1 = ¬A. Using De Morgan's laws, AND and OR can also be constructed from these operators.
Other options, such as XOR with NOT only, generate affine functions and cannot produce non-linear operations required for full functional completeness.